The electoral districts will announce the results of the election recount on Wednesday, 17 April.
The Finns Party ultimately fell only 0.2 percentage points short of upsetting the pre-election favourite, after a late-blooming campaign helped the populist right-wing party win 17.5 per cent of the vote and 39 seats in the Parliament.
In recent months, Finland's far-right Finns Party - previously languishing in fifth place in opinion polls - has surged in popularity to become the second- or third-biggest party, according to recent forecasts.
Finns can expect a broad, ineffective coalition government for the next four years as the Social Democrats, who narrowly won weekend elections, focus on keeping the surging anti-immigration populists out, analysts said.
Rinne also told them: "I have to make a honest confession: I hoped still for a better result".
The Finns Party's previous experience of being in government, when they became the second largest party in the 2015 election, led to the group splitting acrimoniously after its popularity spiralled following unpopular compromises on immigration and European Union bailouts.
The co-ruling Centre Party of Prime Minister Juha Sipila and center-right National Coalition stood at 13.8 percent and 17.0 percent, respectively, marking the first time in a century that no party won more than 20 percent in a general election. After the elections, the composition of the 200-seat unicameral parliament will be determined, a new government will be formed and a prime minister will be appointed.
Greenpeace Finland called Sunday's vote the "climate election", saying that "never before has climate and the limits of planet Earth been discussed with such seriousness in Finland".
The anti-immigration Finns Party also decries the "climate hysteria" of other parties seeking action against global warming.
The nationalist True Finns party came in fourth, with 15.1% of the vote. "The future is a big question for us, all this climate changing, education systems reforming. all kind of things are very important" to Finland's people, he said.
The Finns' stance on environmental policies, which includes an opposition to a proposed tax on meat consumption, appeals to rural voters in particular who fear soaring fuel costs and resent any efforts to change what they see as the traditional Finnish way of life.
"We want a more moderate and sensible climate policy that does not chase industries away from Finland to countries like China", Halla-aho said Sunday at a Helsinki polling station.
It referred to a recent nationwide poll where a whopping 70% of the respondents said tackling climate change and reducing carbon footprints should be one of the new government's key priorities.
Reform has been controversial in Finland and plans to cut costs and boost efficiency have stalled for years, leaving older voters anxious about the future. Finnish lawmakers last month voted to phase out burning coal as an energy source to end it by 2029.